A132283 Normalization of dense fractal sequence A054065 (defined from fractional parts {n*tau}, where tau = golden ratio).
1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 9, 1, 6, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9, 1, 14, 6, 11, 3, 8, 13
Offset: 1
Keywords
Examples
Start with A054065=(1,2,1,2,1,3,2,4,1,3,5,2,4,1,3,5,2,4,1,6,3,5,2,...) Step 1. Append initial 1. Step 2. Write segments: 1; 1,2; 1,2; 1,3,2,4; 1,3,5,2,4;... Step 3. Delete repeated segments: 1; 1,2; 1,3,2,4; 1,3,5,2,4; ... Step 4. Make segment #n have length n by allowing only newcomer, namely n, like this: 1; 1,2; 1,3,2; 1,3,2,4; 1,3,5,2,4; 1,6,3,5,2,4; ... Step 5. Concatenate those segments.
References
- C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
Links
- Clark Kimberling, Self-Containing Sequences, Selection Functions, and Parasequences, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.
Crossrefs
Cf. A132284.
Comments